Solutions of an SU(9) GUT
Abstract
The renormalization group equations for the strong, weak, and electromagnetic coupling constants, at the weak unification scale $M\sb{W} \cong 100$ GeV, are calculated in an $SU(9)$ grand unified theory. These calculations are done for 20 different symmetry breaking patterns in which $SU(9)$ decomposes to $SU(3)\sb{c} \times SU(2)\sb{W} \times U(1)\sb{em}$. Two different $SU(9)$ charge assignments are used, one of which does not possess any exotic fermions. The resulting equations depend upon the mass scales $M\sb{i}$, at which the symmetry breakings occur. Placing the current experimental values for the coupling constants into the equations it is found that very few of these equations possess solutions which give the proper ordering of mass scales: only one symmetry breaking pattern is allowed for the model with no exotic fermions and four are allowed for the exotic fermion model. Those models that do possess solutions do not necessarily have a large "desert" region. It is concluded that the renormalization group equations can provide severe constraints on allowed symmetry breaking patterns in grand unified theories.
Degree
Ph.D.
Advisors
Capps, Purdue University.
Subject Area
Particle physics
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